When You Cross The Streams, Why Don’t Stocks Go To Infinity?

Way back in 1997, the Federal Reserve surprised the financial community with comments relating to the S&P 500 and interest rates.

“The run-up in stock prices in the spring was bolstered by unexpectedly strong corporate profits for the first quarter. Still, the ratio of prices in the S&P 500 to consensus estimates of earnings over the coming twelve months has risen further from levels that were already unusually high. Changes in this ratio have often been inversely related to changes in long-term Treasury yields, but this year’s stock price gains were not matched by a significant net decline in interest rates. As a result, the yield on ten-year Treasury notes now exceeds the ratio of twelve-month-ahead earnings to prices by the largest amount since 1991, when earnings were depressed by the economic slowdown.”

They even went as far as to include a chart of the S&P 500 earnings-price ratio versus US 10-year Treasury note yield.

In the days following the Federal Reserve’s startling stock-earnings-yield-US-Treasury-rate observation, the famed market strategist, Ed Yardeni (then with Deutsche Morgan Grenfell), immortalized this relationship as the “Fed Model.” Although the Federal Reserve has never officially endorsed this model, the name stuck. Not only did it stick, but overnight, Wall Street strategists were busy trying to make sense of the recent divergence that Fed Chairman Alan Greenspan had noted.

Since then, tons of economic wonks have written all sorts of academic papers poking holes in the model, but I kind of think they are missing the big picture. It was never intended to be some sort of comprehensive forecasting tool that could predict future stock index performance. Its use could better be described as a broad barometer that gives a general sense of under or overvaluation of equities versus interest rates. Much like when a doctor uses a thermometer to tell whether a patient is sick or not, it is far from the definitive guide as to the market’s health, but merely one more item for the toolbox.

I don’t want to argue about the problems with the model. Sure, it would be better to use corporate interest rates rather than government rates. And there is no doubt that stocks offer more real return protection while bonds are nominally constrained so the comparison between the two financial assets is definitely flawed.

Yet for all the attempts to discredit the model, too many pundits gloss over the most glaring problem.

According to the model, as interest rates approach zero, the price of stocks approaches infinity.

For example take the current situation. With $130 of earnings-per-share of the S&P 500 and the price of the index at around 2,700, that works out to approximately a 4.75% earnings-yield. If that ratio were to fall to 4%, then the S&P 500 would rise to 3,250. That makes sense. Using a lower discount rate makes the earnings worth more.

But what happens if that rate falls to 2%? The S&P 500 would be 6,500. And at 1%, that number goes to 13,000. As it approaches 0%, the theoretical value of the S&P 500 approaches infinity.

Obviously the model completely breaks down as you approach an interest rate of zero. And then, like most financial theory, the model simply returns an #NA error when rates are pushed into the theatre of the absurd with negative levels.

Yet that doesn’t mean the model is completely useless. Let’s have a look at its behaviour during the last 40 years.

For the last couple of decades of the 20th century, the S&P 500 earnings-yield traded lower than the US 10-year Treasury yield. The two rates would sometimes converge, but would then rectify with S&P 500 earnings-yield falling relative to the US Treasury yield. During this period, you might have argued that stocks were expensive relative to treasuries. Of course it’s not this simple, but on a crude basis, US treasuries still offered some value when compared to the more expensive equities.

Since 2002 the situation has reversed. Whereas before stocks traded with a lower earnings-yield, after the DotCom crash, stocks have traded with a higher earnings-yield than US 10-yr treasuries (a higher earnings-yield implies a lower stock index price).

This might be due to the problem of the model breaking as you approach the zero bound, or perhaps something changed. Maybe it was the beginning of the financial repression that has since enveloped the world. Or maybe it was the disinflation from China joining the WTO and unleashing a huge deflationary wave on the global financial system. Whatever the reason, it’s clear that investors have not bid up stocks as much as the Fed Model would suggest. Investors (and central banks) have pushed up bond prices (lowering their yields), yet have refused to bring stocks along for the ride as much as might be predicted.

Is the Fed Model dead? Or have stocks reflected a more “correct” price as they are not directly influenced by central bank policy?

Instead of just tossing the Fed Model aside as useless and broken, it makes sense to think about how it might once again recouple and provide some guidance for stock market pricing. I just don’t think it’s going to happen by stocks exploding higher towards infinity.

Writing about a subject is the best
way to educate yourself about it, and when I flick through past work I remember how much
they taught me, if no one else. Mainly they taught me that I didn’t know very much. But they
also taught me that most other people didn’t know much either. Thus, some key themes
which stand out include the illusory control of policy makers, the presumed knowledge of
those looking to them to actively do good, the ease with which we fool ourselves, and how
best to protect capital in the face of such unavoidable uncertainty. -- Dylan Grice